A note on face coloring entire weightings of plane graphs

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Given a weighting of all elements of a 2-connected plane graph G = (V,E, F), let f(α) denote the sum of the weights of the edges and vertices incident with the face _ and also the weight of _. Such an entire weighting is a proper face colouring provided that f(α) ≠ f(β) for every two faces α and _ sharing an edge. We show that for every 2-connected plane graph there is a proper face-colouring entire weighting with weights 1 through 4. For some families we improved 4 to 3

@article{StanislavJendrol2014, abstract = {Given a weighting of all elements of a 2-connected plane graph G = (V,E, F), let f(α) denote the sum of the weights of the edges and vertices incident with the face \_ and also the weight of \_. Such an entire weighting is a proper face colouring provided that f(α) ≠ f(β) for every two faces α and \_ sharing an edge. We show that for every 2-connected plane graph there is a proper face-colouring entire weighting with weights 1 through 4. For some families we improved 4 to 3}, author = {Stanislav Jendrol, Peter Šugerek}, journal = {Discussiones Mathematicae Graph Theory}, keywords = {entire weighting; plane graph; face colouring}, language = {eng}, number = {2}, pages = {421-426}, title = {A note on face coloring entire weightings of plane graphs}, url = {http://eudml.org/doc/267708}, volume = {34}, year = {2014},}

TY - JOURAU - Stanislav JendrolAU - Peter ŠugerekTI - A note on face coloring entire weightings of plane graphsJO - Discussiones Mathematicae Graph TheoryPY - 2014VL - 34IS - 2SP - 421EP - 426AB - Given a weighting of all elements of a 2-connected plane graph G = (V,E, F), let f(α) denote the sum of the weights of the edges and vertices incident with the face _ and also the weight of _. Such an entire weighting is a proper face colouring provided that f(α) ≠ f(β) for every two faces α and _ sharing an edge. We show that for every 2-connected plane graph there is a proper face-colouring entire weighting with weights 1 through 4. For some families we improved 4 to 3LA - engKW - entire weighting; plane graph; face colouringUR - http://eudml.org/doc/267708ER -